I'm sorry to hear your treatments are not going well for you. Root Canal therapy is generally quite effective. There are multiple reasons thing can fail and go wrong it's hard to say why your experiencing these problems. Did the same dentist do all the treatment on you? Did you see a specialist for the root canals? How infected (necrotic with abscess) were the teeth before you started? How many steps did the root canals take to complete. During a root canal the dentist is acting as an exterminator, eliminating bacteria and diseased tissue out of the nerve canals, however these canals you see on the xray have thousands of tiny accessory canals branching off of them. This is where the bacteria can hide. The root canals should be shaped properly and during the shaping the root canal should be irrigated or cleaned out well with sodium hydroxide, which penetrates those accessory canals to about 100 microns. In our office we follow up with a laser which penetrates to 1000 microns. This disinfects the tooth inside prior to sealing it off. Some dentists prefer to fill the the tooth with calcium hydroxide to allow penetration of these accessory canals over time, about a month. They then have the patient return to finalize or fill the canal spaces. With severely infected teeth a dentist may add an antibiotic to the treatment protocol immediately following the root canal cleaning and shaping. The sealers used to fill the canals and how well they are packed also play a role in success. We use bc sealer, a bioceramic sealer, and among its excellent properties it does not shrink when setting and has a high pH which continues to resist bacteria growth. If all the steps are done properly root canals have a good success record. I find many root canals also fail because the patients think their procedures are complete when the root canal is done. This is far from the truth. Most dentists put temporary filling material in the top of the tooth following the root canal procedure, expecting to complete the foundation or core and crown the following week. If this temporary stays too long then bacteria will break through and reinfect the tooth. So it is very important to have the core and if needed the crowns put on promptly after root canal treatment. Another way root canals fail is if the tooth was fractured before treatment or even after. Fractured teeth will eventually fail no matter what treatments are done. This is why crowns are suggested on back teeth after root canal therapy. Once the tooth has had treatment it becomes very fragile and subject to fracture, so it is important to crown the teeth as soon as possible to prevent fracture.Next, assuming the root canals were done properly, and the restorations were placed promptly the teeth can still fail if recurrent decay gets under the crown and into the root canal. The restorations may be leaking from improper placement or from poor hygiene or a combination of the two.Finally, perhaps there is a different problem causing your pain. There could be a neurological disorder or sinus problems referring pain to your teeth. As unlikely as this is, its still a factor that should be considered especially if healthy teeth are being subjected to therapy such as extractions, root canals etc.It's very hard to say why things are going wrong for your particular situation. Taking antibiotics over and over is never going to solve your problem as long as the source of the infection remains. Having root canals retreated can be successful and is done all the time, but generally it decreases the success rate by some percent each time it's done. I would find a highly recommended endodontic specialist and dentist in your area for a second and third or forth opinion. It can't hurt to have more then one doctor look at your case. I hope you find a solution to your problem.